December 22, 2017

Fault-tolerant Christmas Trees (not the live kind)

This year's holiday season post brings a bit of graph-theoretic cheer. That's right, there is a type of network called a Christmas tree [1,2]! It is a class of fault-tolerantHamiltonian graph [2,3]. So far, Christmas trees have been applied to computer and communications networks, but may be found to have a wider range of applications, particularly as we move into the New Year.

An example of a Christmas Tree directed graph as shown in [2]. The top two graphs are slim trees of order 3 (left) and 4 (right). A Christmas tree (bottom) includes selected long-range connections (longer than the immediate connection to mother, daughter, or sister nodes).